Question

For the demand equation p = 400-29, verify that demand is elastic and total revenue is increasing for 0<q < 100. Verify that demand is inelastic and total revenue is decreasing for 100 <q<200. pdq Begin by finding in terms of q. The formula for nis n 9 dp (Simplify your answer.) da Since p = 400-29, dp .

Answer 1

SOLUTION,

P= 400-2q..........(1)

This is increasing at  

And decrease at.  

Now, from equation (1)

$\frac{p}{q}= \frac{400-2q}{q}$.................(2)

Then, darivative of equation (1)

$\frac{dp}{dq}= \frac{d}{dq}(400-2q)=-2$

$\frac{dq}{dp}=-\frac{1}{2}$........................(3)

To find the

$\eta =\frac{p}{q}.\frac{dq}{dp}$

$\eta =\frac{400-2q}{q}*\frac{1}{-2}$

$\eta =-\frac{400-2q}{2q}$

$\eta =-\frac{200-q}{q}$

$\therefore \eta =\frac{q-200}{q}$

Answer

$\eta =\frac{q-200}{q}$